Brownian motion on a square Lennard-Jones lattice: Trapping, hopping, and diffusion

We studied the Brownian motion of a single probe particle moving through a square array of fixed lattice particles. Brownian motion was simulated via the dynamic Metropolis algorithm. The probe-lattice particle interaction was the Lennard-Jones potential. In addition to the mean-square displacement and effective diffusion coefficient studied by previous workers, we obtained such diagnostics as the two-point density of states ρ(2)(δr), its angular average ρ2(δr), the correlation function P(δr,τ) for distances δr traveled by probe particles during the elapsed time τ, and the probe dynamic structure function S(k,τ). By varying the temperature and density, we observed distinct diffusive, hopping, and trapping regimes; our computed diagnostics of system behavior reflect different aspects of these regimes in a mutually consistent way